A trolley having mass of 200 kg moves with uniform speed of 36 kmh - 1 on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other ( 10 m away) with a speed of 4 m s -

Question

A trolley having mass of 200 kg moves with uniform speed of 36 kmh - 1 on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other ( 10 m away) with a speed of 4 m s - 1 relative to the trolley in a direction opposite to its inotion and ultimately jumps out of the trolley. With how much velocity has the trolley moved from the time the child begins to run?

TestHub · Accepted Answer

since, no external force is acting on the system, we can apply conservation of linear momentum.

Speed of $200 kg$ trolley $= \frac{36 \times 1000}{60 \times 60} = 10 m s^{- 1}$

If $u$ be the initial velocity of trolley, $v_{b}$ be the absolute velocity of the boy after the beginning of journey of the boy, their relative velocity is $4$ .

So, $v^{'} - v_{b} = 4 \Rightarrow v_{b} = (v^{'} - 4)$

Now, applying law of conservation of momentum,

Momentum before the boy begins tu run
$=$ Momentum after the beginning of boy's running

$\Rightarrow 220 \times 10 = 200 v^{'} + 20 (v^{'} - 4)$

$2200 = 220 v^{'} - 80 \Rightarrow 220 v^{'} = 2280$

$v^{'} = \frac{2280}{220} = 10.36 m s^{- 1}$

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